BEIRUT (AP) — Syrian government forces are carrying out a broad offensive against rebels in the suburbs of Damascus, the state media said Wednesday, as the United Nations appealed for a billion dollars to support rising numbers of Syrian refugees.

The state-run SANA news agency said that troops have killed “scores of terrorists” — the government term for the rebels fighting to topple President Bashar Assad.

The suburbs of the Syrian capital have been opposition strongholds since the uprising started in March 2011. The rebels recently have made significant advances in in the area, capturing air bases and military installation and clashing with a pro-government Palestinian group for control of the Yarmouk refugee camp in the capital’s southern part.

SANA said Wednesday’s fighting was taking place in the capital’s southern outskirts of Daraya, Harasta, Douma and Hajar Aswad, an area neighboring Yarmouk.

On Tuesday, Syrian fighter jets bombed Yarmouk for the second time in a week, sending thousands fleeing from the camp. There were no reports on casualties from those strikes. Similar airstrikes on Sunday killed at least eight people in Yarmouk, activists said.

The rebel offensive in the camp, which began Friday, is aimed at driving out pro-government Palestinian gunmen of the Popular Front for the Liberation of Palestine-General Command.

Most of the fighting on Wednesday was concentrated on surrounding districts outside the camp, the Britain-based Syrian Observatory for Human Rights said. It said the rebels took control of large parts of the camp after resistance from the PFLP-GC gunmen ceased that morning. The group relies on reports from activists on the ground.

Since the camp’s creation in 1957, it has evolved into a densely populated residential district just five miles from the center of Damascus. Several generations of refugees live there, some employed as doctors, engineers and civil servants and others as day laborers and street vendors. Many Syrians also have moved into the camp area over the years.

When the revolt against Mr. Assad’s rule began 21 months ago, the half-million-strong Palestinian community in Syria stayed on the sidelines. But as the civil war deepened, most Palestinians backed the rebels, while some groups — such as the PFLP-GC— have been fighting alongside the troops. The group is led by Ahmed Jibril, Mr. Assad’s longtime ally.

The fighting in the camp has forced an exodus of Palestinian refugees and Syrians who came to the camp in past weeks to escape violence elsewhere in the city, according to U.N. officials.

More than two-thirds of the roughly 150,000 Palestinian residents of Yarmouk have left the camp since Friday, when the fighting flared up, according to the U.N. Relief and Works Agency for Palestine Refugees. They have either sought shelter in the outskirts of the camp, in other parts of Damascus or other Syrian cities, or headed to the Syrian-Lebanon border, said Sami Mshasha, an UNRWA spokesman.

Palestinian President Mahmoud Abbas said in a statement Wednesday he had asked U.N. Secretary-General Ban Ki-moon to help in bringing the Palestinian refugees in Syria to the Palestinian territories. This could include the West Bank, where Mr. Abbas governs, or the Hamas-ruled Gaza Strip.

The statement said there are 450,000 Palestinian refugees living in 10 camps in Syria. Mr. Abbas said Yarmouk, which is the biggest camp, “has been through a difficult situation due to the escalating conflict in Syria.”

Any movement of refugees into the West Bank would need the consent of Israel.

Israel’s Foreign Ministry had no comment.

The 21-month battle to bring down the Assad regime has forced some 3 million Syrians from their homes, according to a new estimate. Cold, wet winter weather is making life increasingly difficult for the displaced. Among those who left their homes are more than 500,000 who fled to neighboring countries.

In Geneva, the U.N. refugee agency appealed to international donors for $1 billion to support Syrians in neighboring countries and Egypt. Additionally, the United Nations also is appealing for more than $500 million dollars to help people inside Syria who have been driven from their homes during the civil war.

The new appeal is based on planning estimates that up to 1 million Syrian refugees will need help during the first half of 2013.

“Unless these funds come quickly we will not be able to fully respond to the lifesaving needs of civilians who flee Syria every hour of the day — many in a truly desperate condition,” said Panos Moumtzis, the agency’s regional coordinator for Syrian refugees.

Children make up almost half of the refugees crowded into camps and host communities across five countries, and their numbers rise inexorably, the statement also said.

About 525,000 Syrians either are registered as refugees or are being assisted in Turkey, Lebanon and Jordan. This is a seven-fold increase since May, when 70,000 Syrians registered for help. Many more Syrians are in Turkey, Lebanon, Jordan, Iraq and Egypt but have not yet registered, the Office of the U.N. High Commissioner for Refugees said in a statement Wednesday.

Since July, Syrian refugees have fled the conflict for neighboring countries at a rate of 2,000 to 3,000 a day, the agency said.

More than 40,000 people have been killed in Syria since the revolt started in March 2011 as mostly peaceful demonstrations against Mr. Assad’s rule. It morphed into a civil war after some members of the opposition took up arms to fight a brutal government crackdown on dissent.

• Associated Press writer Albert Aji in Damascus and John Heilprin in Geneva contributed to this article.